FLIGHT CREW OF SMALL TURBOJET TRANSPORT FAILS TO REMAIN EAST OF ORD 345 RADIAL ON PAL-WAUKEE 2 SID FROM PWK.

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I PERSONALLY COPIED OUR CLRNC FROM CLRNC DELIVERY AT PWK. THE CLRNC INCLUDED THE PAL-WAUKEE 2 DEP WITH RADAR VECTORS TO EON. WE WERE NOT GIVEN A HDG FOR THE DEP PROC AT THAT TIME; BUT DID BRIEF THE PROC AS A CREW. PRIOR TO ENTERING THE RWY FOR DEP I TUNED THE ORD VOR (113.9) AND SET UP THE 345 DEG RADIAL ON MY (THE COPLT'S SIDE) HORIZ SITUATION INDICATOR TO BACK UP THE PROC REQUIREMENTS WITH RAW VOR DATA. AFTER A SHORT DELAY; WE WERE CLRED INTO POS AND HOLD AND TOLD THAT A LEARJET WAS ON AN 8 MI FINAL FOR RWY 16 ON THE ILS. WE WERE CLRED FOR TKOF WITH A R TURN TO A HDG OF 040 DEGS VIA THE PAU-WAUKEE DEP. AFTER TKOF AND AT THE END OF THE RWY CAPT BEGAN A R TURN WITH APPROX 35 DEGS OF BANK. WHILE CLBING IN THE TURN CHICAGO DEP ADVISED THAT WE NEEDED TO 'TIGHTEN UP THE TURN' FOR TFC AT O'HARE. I ACKNOWLEDGED WITH OUR TAIL NUMBER AND LOOKED AT MY COURSE DEV INDICATOR WHICH AT THE TIME STILL SHOWED THAT WE WERE ON THE PROPER SIDE OF THE ORD VOR AS PER THE DEP PROC. THE CAPT ALSO INCREASED THE BANK TO APPROX 45 DEGS AT THE SAME TIME. AS WE WERE LEVELING OFF AT 3000 FT ALT CHICAGO DEP AGAIN ADVISED US THAT THEY NEEDED A TIGHTER TURN. AGAIN WE VERIFIED THAT WE WERE STILL ON THE PROPER SIDE OF THE VOR; ALTHOUGH DUE TO OUR CLOSE PROX TO THE VOR THE DEV INDICATOR WAS NOW FLUCTUATING L AND R OF THE 345 SET COURSE. WE CONTINUED THE TURN TO OUR ASSIGNED HDG OF 040 DEGS WITH NO TFC ALERT OR RA. AFTER BEING HANDED OFF TO THE NEXT CTLR WE WERE ADVISED THAT WE NEEDED TO CALL ABOUT A POSSIBLE PLTDEV. SEVERAL MINS LATER WE WERE HANDED OFF TO A 3RD CHICAGO CTLR. THIS 3RD CTLR ON FREQ 128.525 INFORMED ME THAT WE COULD DISREGARD THE REQUEST TO CALL GIVEN BY THE PREVIOUS CTLR AND THE ISSUE HAD BEEN 'RESOLVED.' I FEEL THAT THE MOST OBVIOUS CONTRIBUTING FACTOR TO THIS POSSIBLE DEV WAS THE DELAY IN PROVIDING WHAT HDG WOULD BE ASSIGNED ON DEP. AS A CREW MEMBER WAITING IN POS ON THE RWY WITH ANOTHER ACFT ON FINAL BEHIND ME; WE WERE NOT PROVIDED ADEQUATE TIME TO DETERMINE IF THE ASSIGNED HDG COULD BE COMPLETED PRIOR TO THE RESTRICTING RADIAL. THE PROC DOES INDICATE THAT THE PLT SHOULD NOTIFY ATC IF UNABLE TO COMPLETE THE TURN WITHIN THE PRESCRIBED RADIAL; BUT NOT WHAT HDG YOU WOULD BE TURNING TO. BECAUSE THE TURN PLACES THE ACFT SO CLOSE TO THE VOR; ADEQUATE COURSE INFO IS NOT AVAILABLE FOR MOST OF THE PROC. AT NO TIME DURING THE EVENT WHEN POSITIVE COURSE GUIDANCE WAS AVAILABLE DID I SEE THAT WE HAD CROSSED THE BOUNDARY RADIAL; BUT FOR A SHORT (AND MOST CRITICAL) PORTION OF THE PROC THE ACFT IS IN THE VOR 'CONE OF CONFUSION' AND A DEV MAY HAVE OCCURRED DURING THAT TIME BUT IT COULD NOT BE DETERMINED FROM THE INFO WE HAD IN THE COCKPIT. THE ACFT WE WERE FLYING IS CAPABLE OF FLYING THE PUBLISHED DEP PROC SAFELY DEPENDING UPON THE ASSIGNED HDG BUT THAT HDG WAS GIVEN TO THE CREW TOO LATE TO MAKE THE DETERMINATION TO REJECT THE DEP PROC IN MY VIEW. THE PROC ALSO CALLS FOR A LEVELOFF AT 3000 FT WHICH INCREASES THE WORKLOAD OF A HIGH PERFORMANCE JET WHEN COMBINED WITH THIS STEEP-BANK TURNING DEP PROC. SUPPLEMENTAL INFO FROM ACN 811904: I THEN PLACED THE ACFT IN A 45 DEG BANK AND CONTINUED THE CLB TO 3000 FT; AIRSPD AT THIS TIME WAS APCHING APPROX 230 KTS.